bands,[59],[60],[61] play an insignificant role in these structures due to an inter cone spacing that is much larger than the optical wavelength. Consequently, each microcone acts as an independent optical antenna and waveguide, consistent with previous findings [62],[63],[64].
The high absorption arises from a combination of coupling into waveguide modes and the length of the microcones. Many groups have studied and demonstrated enhanced absorption in Si nanowire arrays due to coupling into waveguide modes with large extinction cross sections.[65],[66],[67],[68],[69] Owing to nanofabrication-imposed limitations to the achievable nanowire aspect ratio, the Si nanowire array absorption is typically much lower than that for optically thick planar Si absorbers, despite field enhancements due to the material volume required to achieve near-unity absorption in indirect bandgap materials [70]. Our microcone structures also capitalize on waveguide modes for optical absorption enhancement, while simultaneously incorporating long optical path lengths to achieve near-unity absorption. Efficient coupling into the optical waveguide modes of the Si microcone is the critical factor in the remarkable optical properties of these arrays.
Three-dimensional full field electromagnetic wave simulations of microcone arrays were performed to characterize the waveguide modes. Rigorous 3D full field electromagnetic wave FDTD simulations of microcone arrays were performed using a commercial software package, Lumerical FDTD. The arrays were constructed using the 3D rectangular simulation region with periodic boundary conditions along x and y axes to depict 7 µm square lattice of the arrays, and infinite boundary conditions rendered as perfectly matched layers (PML) along z axis. In the simulation region microcones had a top diameter of 50 nm, bottom diameter of 7 µm, and height of 75 µm.
Palik material data provided by Lumerical was used for modelling the material as Si. Single wavelength infinite plane wave sources at four different wavelengths (400 nm, 600 nm, 800 nm, and 1000 nm) were used with a long pulse time of 50 fs to simulate steady state behavior. Generation rate in these structures was calculated by using the built in CW-generation (continuous wave generation) rate analysis group to obtain electron hole pair generation profiles under steady state illumination. Figure 3.7 displays carrier generation cross-sections for microcones at incident wavelengths of 400, 600, 800, and 1000 nm, respectively. Figure 3.7 (e)-(h) show complete cone cross sections on a logarithmic scale, marked with light blue squares indicating the bounds of Figure 3.7 (a)-(d), which focus on the upper portion of the cone and are shown in linear scale.
All absorption profiles indicate light coupling into waveguide modes, but the modes are less obvious at λ = 400 nm (Figure 3.7 (a) and (e)), due to strong absorption above the direct gap of Si. Below the direct gap of Si, the waveguide characteristics become more apparent. Absorption occurs primarily in the microcone core, indicative of guided mode propagation in the cone, and exhibits semi-periodic longitudinal intensity oscillations that scale with incident wavelength; these longitudinal oscillations in field intensity are not representative of any longitudinal interference modes, but rather are indicative of the phase cycle of mode propagation. This distinction is critical because longitudinal interference modes would require long solar coherence lengths, whereas mode propagation does not.
Figure 3.7: Longitudinal cross sections of power absorption for Si microcones at 400 (a,e), 600 (b,f), 800 (c,g), and 1000 (d,h) nm wavelengths, respectively; (a-d) upper portion of microcone with linear intensity scale; (e-h) complete microcone with logarithmic intensity scale; light blue squares correspond to expanded cross sections in (a-d); different relative scales are used for each figure to highlight modes.
Additionally, the existence of significant intensity near the lower end of the microcone in the λ = 1000 nm profile demonstrates long distance waveguide mode propagation to the bottom of the microcone, enabling near-unity absorption for wavelengths near the Si band edge. Simulations show that the reflection is < 1 % at wavelengths below 1000 nm agreeing with the measurements. Since carrier generation was observed to occur predominantly in the upper portion of the cones, the minor deviation from perfectly circular cone shape seen in Figure 3.2 at the base of the cones is not expected to give rise to a significant change in the optical properties relative to the circular cross sections assumed in our simulations.
Figure 3.8: Detailed mode analysis of upper portion of a microcone at λ = 1000 nm; mode color key in (h) is applied throughout the figure; (a) longitudinal absorption cross section with dashed lines indicating radial cross sections; (b-g) radial cross section, exhibiting HE1n modes; (h) traditional dispersion curves for HE1n modes for n=3.577; (i) non-traditional dispersion curves, converted from (h) for λ = 1000nm.
Detailed mode analysis reveals that light couples into the set of first azimuthal order waveguide modes, HE1n, as illustrated for λ = 1000 nm illumination in Figure 3.8. As previously reported,[71],[72] efficient coupling occurs into this set of modes due to the strong overlap in symmetry between the incident plane wave and the in-plane mode field profiles. Figure 3.8 (a) displays a longitudinal cross section marked with horizontal dashed lines colored to indicate their correlation with the radial cross sections in Figure 3.8 (b)-(g); the radial cross sections correspond to the first six HE1n modes, in ascending order. As expected, the first order HE11 mode appears at the top of the wire, and the higher order modes appear in sequence, as radius increases.
(1)
The dispersion curves for these modes were calculated from the eigenvalue equation (Eqn. 1) for cylindrical dielectric waveguides,[73] where Jm and Hm are the cylindrical Bessel and Hankel functions of the mth order, k0 is the free space wavevector, kcyl(kout) is the transverse wavevector inside(outside) the cylinder, β is the mode propagation constant, εr,cyl (εr,out) and µr,cyl(µr,out) are the relative dielectric permittivity and permeability inside(outside) the cylinder, and a is the cylinder radius. Figure 3.8 (h) and Figure 3.8 (i) show the dispersion curve for a Si waveguide (n=3.577), in its tradition form, k0a(βa), and a non-traditional form, mode index vs. radius, respectively. The mode color key in Figure 3.8 (h) is consistent throughout the figure. The dashed lines on Figure 3.8 (i) indicate the radius of the mode cross sections in Figure 3.8 (b)-(g), revealing that the modes are most prominent between a mode index of 1 and 2. This moderate mode index is due to a tradeoff between ease of free space coupling and mode confinement mediated-absorption. Mode profiles, propagation constants and radius range are all consistent with analytic waveguide theory. These observations demonstrate the critical role of waveguide modes in the optical characteristics of the microcone arrays.
Photogenerated Carrier Lifetime Measurements
In order to evaluate quality of etched microcones/microwires and estimate the maximum achievable Voc, transmission electron microscopy (TEM) and lifetime measurements were performed. Etched microwires were removed from the host Si wafer by mechanical cleaving with a razor blade before being dispersed in isopropyl alcohol. The resulting solution was spun onto a Si wafer for 30 s at 2000 rpm. The wire-coated wafer was then coated with ~ 20 nm of Al2O3 with atomic layer deposition.
Axial cross sections were made in a FEI Versa dual-beam focused ion beam instrument, extracted with an FEI EasyLift NanoManipulator and welded to an Omniprobe Cu liftout TEM grid before Figure 3.9: Transmission electron microscopy (TEM) study of a single etched microwire immediately after ICPRIE with the Al2O3 mask intact on top and with no cleaning except a solvent rinse is aligned to the 001 zone axis. A large area corresponding to the tip of a cone was studied (far left). Bright field images (BF) are devoid of contrast within the etched wire other than bend contours introduced during sample preparation, and selected area diffraction (SAD) shows a clean pattern.
Higher resolution images at the top of the cone (center) shows no evidence of damage to the cone tip which was protected by the hard mask during growth. However, a high resolution imaging reveals a thin (~ 2-3 nm) region on the sidewalls (far right) which could correspond to damage introduced during the etching process. These data were collected at 300 kV in an FEI Technai TF30 TEM.
thinning to electron transparency. Electron microscopy images of the sidewall shown in the Figure 3.9 shows minimal surface damage due to etching, and no lattice damage in the bulk, as expected from the low forward power (5W) and predominantly chemical nature of the dry etching process.
In order to estimate the recombination at the surface of etched microwires, cylinders of 3, 15 μm diameters and height 50, 70 μm respectively were etched by ICPRIE in high lifetime (~1 ms) intrinsic Si wafers. Standard RCA 1 and RCA 2 clean processes followed by 20s damage removal in 5.4M KOH solution at around 70oC were performed on the etched samples. Microwires from these substrates were scraped off their substrates with a razor blade and were collected in a centrifuge tube.
A further 10s etch in 3.6M KOH solution at room temperature is performed on these microwires to remove the back surface damage due to scraping, before neutralizing the etching solution to stop etching by addition of concentrated 5.8M HCl. The microwires were separated from the resulting solution by centrifuging the solution. The wires were rinsed three times in DI water to get rid of the solution. Various liquid passivation mechanisms including 3.6M HCl solution, 31.8M HF, 1.3M HF, and Iodine in Ethanol were added to the cleaned wires. Lifetime measurements of these wires were performed by a home built microwave detected photoconductivity decay (MW-PCD) tool with Nd:YaG laser illumination at 1064 nm as shown in Figure 2.10. Laser power was varied between 30-120 μJ. Pulse width of 5 ns and spot size of 3 mm diameter was used at 50 Hz frequency during measurements.
Figure 3.10: Schematic of home built microwave detected photoconductivity decay setup
While it is most informative to measure the lifetime at different, known injection levels, it is difficult to know the exact injection level in this configuration. 1064 nm is weakly absorbing in silicon, and therefore significant attenuation in intensity is not expected as light is absorbed. It is likely that some distribution of injection levels exist due to their varying optical environments. The injection level, and therefore the most relevant recombination mechanism can be estimated by measuring the change in lifetime as a function of laser intensity. All samples showed an increase in lifetime as pulse energy was increased from 30 μJ to 120 μJ, characteristic of transition from low level injection to high level injection [74].
Table 3.1 compares the various surface passivation mechanisms under which the carrier lifetimes were measured in 15 μm diameter, and 70 μm long silicon microwires at a laser pulse energy of 240 μJ. Under 3.6 M HCl passivation a lifetime of 1.9 μs was measured in these microwires. Similar measurement for 3 μm diameter, and 50 μm long microwires measured carrier lifetimes of 0.67 μs.
HCl is known to remove metallic impurities from silicon and therefore is used in processes such as RCA 2 cleaning. Therefore we hypothesize that HCl does a better job of removing the metallic impurities that contaminate the silicon microwires during the scraping off process using a metallic razor blade. Table 3.2 shows the estimated carrier lifetimes in the 3 μm and 15 μm diameter microwires under various surface recombination velocities assuming a bulk lifetime of 1 ms under low level injection conditions calculated from Synopsis Sentaurus TCAD simulations. The carrier lifetimes measured indicated that the surface recombination velocities at the surfaces were of the order of few hundreds of cm/s.
Passivation Mechanism
Carrier Lifetime (μs) Iodine in Ethanol 0.6
1.3 M HF 0.4
31.8 M HF 0.7
3.6 M HCl 1.9
Table 3.1 : Carrier lifetimes measured under various surface treatments
The carrier recombination lifetimes were measured for microcone arrays passivated by Al2O3 coated- by atomic layer deposition (ALD) [37, 75]. Al2O3 was deposition on Si by atomic layer deposition using Trimethylaluminum and water as precursors at 150oC after standard cleaning procedure. The precursors were pulsed for 15 ms at 20 s intervals for 200 cycles. The Si samples then annealed at 400oC for 10 minutes under nitrogen flow of 3 lpm. Al2O3 passivated tapered microwire arrays were embedded in PDMS and peeled from their respective substrates using a razor blade. During the measurements, the fractured back surfaces of the peeled microwires were passivated in situ using 5.8M HCl, after a 20s damage removal etch in 3.6M KOH at room temperature. All the lifetime measurements resulted in continuously increasing lifetimes as a function of intensity, indicating that
Wire Geometry:
Diameter (d μm) Height (h μm)
SRV (cm s-1) Calculated Lifetime (μs)
d = 3 50 4
h = 50 100 1.5
500 0.75
d = 15 20 16.5
h = 70 100 6
500 1.5
Table 3.2: Estimated lifetimes based on SRVs
Figure 3.11:Microwave reflectivity of ALD Al2O3 passivated microcone arrays with in situ back surface passivation using 5.8M HCl measured using the microwave photoconductivity setup with 0.75 µs carrier lifetime
measurements were done at the onset of high injection level [76]. Lifetimes of 0.75 µs were measured in these arrays with 240 µJ pulses as shown in Figure 3.11.
An analytical model was implemented to estimate surface recombination velocity (SRV), implied Voc, and the corresponding maximum limiting efficiency achievable from the carrier lifetime measurements. The model was implemented in Microsoft Excel, using VBA to iteratively solve the transcendental equations for steady state carrier concentration. Equivalent planar thickness, surface area, total absorption, surface recombination velocity, radiative recombination coefficient, Shockley-Reed-Hall coefficients [77], and auger recombination coefficients[78] in the bulk were input parameters. This model gives the absolute theoretical maximum limiting Voc, and efficiency that can be achieved in principle from the microcone light trapping structures with the measured lifetimes. The average steady state excess carrier concentration was obtained by solving for equivalence of the total generation rate and sum of all recombination rates due to the four recombination mechanisms considered. In this model we ignored the effects of resistances and assumed a narrow selective contact, therefore the change in quasi fermi levels in the bulk of Si is very small. The quasi fermi level separation and maximum Voc achievable are obtained from equation 2. To estimate the total carrier generation, an internal quantum efficiency of 100 % was assumed, and the total photon flux absorbed was calculated from the measured absorption in tapered microwire arrays under AM 1.5 spectrum. Because the etching process was predominantly chemical and no bulk damage was observed in TEM analysis, the bulk lifetime was assumed to be 1 ms (same as the lifetime measured in the starting wafer in which the structures were etched into). Finally, an efficiency was extracted using the total generation as the Jsc and calculating a fill factor using the empirical model for a device without series resistance or shunting developed by M.A. Green [79].
In this model an intrinsic doping density (ni) of 9.7 x 109 cm-3, donor doping density (Nd) of 1017 cm-
3, and radiative recombination coefficient (Brad) of 4.7 x 1015 cm3s-1 were used. This model provides an estimate for the absolute maximum achievable efficiency. In realistic photovoltaic devices, resistances are expected to reduce the efficiencies relative to those calculated via this model.
𝑉𝑂𝐶 = 𝐸𝑓𝑛− 𝐸𝑓𝑝 = 𝑘𝑇
𝑞 ln ((𝑁𝐴+ ∆𝑛)∆𝑛
𝑛𝑖2 ) (2)
The SRV achieved was estimated to be 150 cm s-1, with the corresponding implied Voc to be 0.655 V, and the maximum efficiency achievable to be 22.2 %. The microcone arrays are surface
recombination limited and a further decrease in SRV to 5 cm s-1 is shown to enhance the lifetime to
> 15 µs, and the maximum limiting efficiency to > 25%.
Conclusion
In conclusion, the microcone arrays fabricated in this work demonstrate superior light trapping properties with < 1 % angular averaged reflection, and absorption reaching the 4n2 light trapping limit due to enhanced coupling of incident light into the waveguide modes. The high absorption arises from a combination of coupling into waveguide modes and overall length of the microcones, resulting in absorption that approaches to the ray optic light trapping limit over most of the solar spectrum and absorption above the ray optic limit at wavelengths near the Si energy band gap [80],[81]. These microcones show no bulk damage and minimal surface damage that can be removed by surface cleaning after fabrication. We measured carrier lifetime in these microstructures by microwave detected photoconductivity measurement, and measured lifetimes of 0.75 µs for wires under ALD deposited 20 nm thick Al2O3 sidewall passivation with 5.8 M HCl back surface passivation. In this work the performance of the arrays is limited by surface recombination and therefore further improvement in surface passivation methods to these arrays can push the performance of these arrays to reach Voc > 0.7 V and maximum possible efficiency > 25%. The efficiencies estimated by our model provide the absolute maximum possible limiting value that are in principle achievable given the material volume and surface area of the fabricated structure and the observed optical properties. The real world device architectures we envision utilizing these microcone arrays include all back contact solar cells[37, 43, 75, 82] similar to previous demonstrations with an ultrathin Si substrate [83] or as a flexible solar cell with a conventional back contact and a transparent front contact [56], the effect of resistances in the structures and selective contacts are expected to reduce the estimated efficiency further. In this study, ICPRIE was chosen as the fabrication technique because it offers significant optoelectronic performance advantages-- the electronic quality of the bulk wafer is preserved, and the fine control over the shape of etched structures enables optimal optical design. Due to the high surface area and superior light trapping these microcones are also excellent candidates for applications in photoelectrochemical cells and enhancing electrode efficiencies [84-88].
Photoelectrochemical Profiling Photoinduced Carrier Generation in Silicon Microwires
Introduction
Semiconductor mesostructures have been studied extensively due to their unique band gap energies, absorption and reflectance properties, charge-transport pathways, and increased surface area, relative to their planar counterparts.[89-92] The ability to tailor such properties has made mesostructures attractive architectures for applications in areas including photonics[93-95], photovoltaics[96-99], electronics[100, 101], catalysis[102-104], and sensing[105, 106]. Mesostructured semiconducting wire arrays composed of elemental, binary compounds (e.g. group III-V, II-VI, IV-VI) and ternary compounds have been synthesized.[92, 107-114] The macroscopic optoelectronic and electrochemical properties of such wire arrays have been experimentally characterized[115-119], but nanoscale analyses that aim to provide a microscopic understanding of these properties have been mostly limited to theoretical and computational methodologies.[120-123]
The optical excitation of photoactive semiconductor substrates immersed in a metal-ion solution can provide the driving force for deposition of a metal.[124] Photoelectrochemical metal deposition has been used to generate arbitrarily patterned metallic deposits on a semiconductor surface by use of a photomask or by use of scanning laser illumination.[125-129] The localized illumination results in the spatially confined generation of mobile charge-carriers that are transported toward the solid/solution interface, and subsequently drive localized electrochemical deposition. Herein, we demonstrate the use of such a photoelectrochemical deposition process to physically record the localization of carrier generation in three-dimensional semiconductor mesostructures under conformal illumination. Unlike planar materials, such structures display significant, inherent spatially anisotropic and complex, light absorption in three dimensions.[122, 123] Si microwire arrays can be grown with a high degree of fidelity and control; provide superior optical absorbance
on a per unit mass basis than planar Si; and have shown potential for use in photovoltaic, fuel- forming photoelectrochemical, and sensing applications.[88, 130-133] In this work, Au was photoelectrodeposited onto arrays of cylindrical or tapered Si microwires, using a series of narrowband light sources providing excitation at a variety of wavelengths. The localization of the Au deposition was examined by scanning-electron microscopy (SEM). Computer modeling of carrier generation in the same structures was performed to correlate the localization of the deposition with the expected spatial distribution of the carrier generation in the material.
Experimental Procedure
S1813 positive photoresist was spin coated at 4000 rpm onto the top of Si wafers. The wafers were then heated on a hotplate at 115 ºC for 1 min. The photoresist was then exposed using UV illumination through a square lattice mask consisting of holes with a 3 µm diameter and a 7 µm pitch.
The photoresist was developed using MF-319 developer and the wafers were baked for 10 min at 115 ºC. A 200 nm thick Al2O3 mask was then deposited onto the patterned wafer using electron- beam evaporation. PG-remover was used to liftoff the photoresist. After the liftoff, Fomblin oil was applied to the back of the wafers to act as a thermal contact material, and the wafers were loaded into the etching chamber. Wires were etched using a cryogenic inductively coupled plasma reactive ion etching process (ICP-RIE) with an Oxford DRIE 100 ICP-RIE system. Etching was performed at low capacitive coupled power of 5 W to reduce damage due to the momentum of the ions. A high inductively coupled power of 900 W was used to increase the number of ions in the plasma to achieve high rates of chemical etching. The chamber was maintained at -120 ºC and a pressure of 10 mTorr during the etching process. Etching was performed using SF6 : O2 ratios ranging from 70 sccm : 5.5 sccm to 70 sccm : 8 sccm for 30 min. Variation of the O2 concentration in the plasma enabled control over the wire taper. After etching, the wafers were dipped in buffered HF to chemically remove the Al2O3 mask.
Si microwire arrays were cut into ~ 1 cm x 1 cm sections. Immediately before deposition, each section was rinsed with CH3OH, followed by H2O, and then immersed in buffered HF(aq) for ~ 60 s to remove any surficial SiOx from the Si. The sample was then rinsed with H2O and dried with a stream of N2(g). A Ga/In eutectic was scratched into the back side of each section using a carbide